I am going to partially disagree with the first answerer. 'I'd love...' can be used in this context, it expresses a stronger desire than 'I'd like...' However, 'I'd love to do x' is often, but not always, followed by a reason that I am unable to do x e.g. 'I'd love to invite you to take part in/ get involved in the activity about our traditional culture, but unfortunately I can't because all the places are taken.' The second part of your sentence is correct. In summary both your options are correct, and you can use 'I'd love to...', but 'I'd like to...' is probably commoner, is not as strong and would not leave the person being invited waiting for 'but...'

Good morning, Mrs. Heidi. First of all, let me correct you. The correct form is "I'd like to invite you". The other both forms, such as "to take part in/get involved" are correct. Have a nice day!